Originally Posted by
Em Yeu Anh Question: Expand $\displaystyle \frac{1}{(1+x)^\frac{1}{4}} $ as a power series and use it to estimate $\displaystyle \frac{1}{1.1^\frac{1}{4}} $ correct to three decimal places.
I am clueless!
Also check out "Binomial Theorem" on Wikipedia. Rising factorial, falling factorial, I'm confused. How about I show you this Mathematica code and then you figure out how I got it and what it means.
Code:
n[858]:=
myFunctions[x_] := 1/(1 + x)^(1/4)
mySeries[x_, n_] :=
Sum[(FactorialPower[-4^(-1), k]/k!)*
x^k, {k, 0, n}]
mySeries[0.1, 20]
myFunctions[0.1]
Out[860]=
0.9764540896763106
Out[861]=
0.9764540896763105